Not your screen monkey (he/him)
I can't say I'm a fan, in the main.Therefore, I present the following proposal:
1d4 - Wizards, Sorcerers.
1d6 - Warlock, Clerics, Bards and Druid.
1d8 - Paladins and Rangers.
1d10 - Rogue and Monk.
1d12 - Fighter and Barbarian.
The current HD have a lot to do with legacy issues - all of the fighters subclasses are d10s, cleric subclasses d8s, etc. But they also indicate designs of how that particular class was expected to fight. If their class can be expected to stand their ground and defend their fellows in back ranks - fighters, paladins - they get a d10 (barbarians were a particular exception). Or are they expected to move around and avoid that kind of protracted entanglement - monks, rogues - they get a d8. Half-caster vs non-caster never really entered into it - nor do I think it necessarily should, particularly if the half-caster spells are focused around supporting their fighting role rather than casting like a wizard or sorcerer.
A d4 for hit die isn't, I think, sustainable in 5e for long. The damage amounts dealt by monsters and NPCs have been higher since 3e thanks to everyone getting stat bonuses to damage now. The d4 for hit points was due for retirement.